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Cosserat生长弹性杆动力学的Gauss最小拘束原理
  • ISSN号:1000-0887
  • 期刊名称:《应用数学和力学》
  • 时间:0
  • 分类:O316[理学—一般力学与力学基础;理学—力学]
  • 作者机构:[1]上海应用技术学院机械工程学院,上海201418, [2]上海大学理学院力学系,上海200444
  • 相关基金:国家自然科学基金(11372195;10972143)
中文摘要:

以自然界中具有生长、变形和运动特征的细长体为背景,用经典力学中的Gauss最小拘束原理研究生长弹性杆的动力学建模问题.在为生长弹性杆动力学建模提供新方法的同时,扩大了Gauss原理的应用范围.以Cosserat弹性杆为对象,分析弹性杆生长和变形的几何规则,表明生长应变和弹性应变是非线性耦合的;本构方程给出了截面的内力与弹性变形的线性关系;利用逆并矢,将经典力学中的Gauss原理和Gauss最小拘束原理用于生长弹性杆动力学,得到等价的两种表现形式,反映了时间和弧坐标在表述上的对称性,由此导出了封闭的动力学微分方程.给出了两种形式的最小拘束函数,表明生长弹性杆的实际运动使拘束函数取驻值,且为最小值.最后讨论了生长弹性杆的约束与条件极值等问题.

英文摘要:

The dynamic modeling of growing elastic rods,with the background of a kind of growing,deforming and moving slender bodies in nature and engineering,was studied based on the Gauss principle of least constraint in the classical mechanics. This provides a newmethod for the dynamic modeling of growing elastic rods,and meanwhile expands the application scope of the Gauss principle of least constraint. With the Cosserat growing elastic rod as the object,the geometric rules for growth and deformation of the rod were analyzed,which showthat the growing strain and elastic strain are in a nonlinear coupling relation. The constitutive equations were given as a linear relationship between the internal forces and elastic deformations of the rod's cross section; through definition of the inverse of dyad,the Gauss principle of least constraint was used to model the growing elastic rod dynamics and get 2 equivalent forms of the Gauss variation,which reflect the symmetry between time and arc coordinates in the expression of rod dynamics. The closed-form dynamic differential equations were derived. 2 forms of constraint functions were given,which indicate that the actual motion of an elastic rod made the function at a stationary value,and also the minimum value. Finally,some problems about the constraints and conditional extremums of the growing elastic rod dynamics were discussed.

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期刊信息
  • 《应用数学和力学》
  • 中国科技核心期刊
  • 主管单位:重庆交通大学
  • 主办单位:重庆交通大学
  • 主编:钟万勰
  • 地址:重庆南岸区重庆交通大学90信箱
  • 邮编:400074
  • 邮箱:applmathmech@cqjtu.edu.cn
  • 电话:023-62652450
  • 国际标准刊号:ISSN:1000-0887
  • 国内统一刊号:ISSN:50-1060/O3
  • 邮发代号:78-21
  • 获奖情况:
  • 国际工程索引(EI)收录期刊,我国力学类核心期刊,中国期刊方阵“双效”期刊
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论(网络版),日本日本科学技术振兴机构数据库,美国应用力学评论,中国中国科技核心期刊,中国北大核心期刊(2004版),中国北大核心期刊(2008版),中国北大核心期刊(2011版),中国北大核心期刊(2014版),中国北大核心期刊(2000版)
  • 被引量:8965